Math literacy and metacognition: Swapping repetition for reflection

During my six years teaching math in higher education, my colleagues and I often spoke about how we only truly understood a topic once we had taught it.

I believe this is because the more you communicate math, the clearer your understanding of it becomes. Preparing to teach a course means taking the time to reflect on your own understanding of the material and consider the different ways you can explain a concept. This is known as metacognition.

Simply put, metacognition refers to thinking about one’s thinking.

Applying metacognitive techniques can be highly effective in helping students to learn better and achieve subject mastery – a view promoted by contemporary educational research. 

With math continuing to experience an engagement problem in many countries, there is an opportunity to do better. Instead of meeting students where they are, the focus due to teaching pressures is often on covering the course material. When combined with limited class time for personalized tuition, much student thinking is dedicated to memorization and going through the motions of carrying out computations. 

Better mathematical literacy

Happily, a mindset shift is underway in the understanding of the ‘what and how’ of math teaching. It’s an exciting time as we move towards a more equitable approach that meets the needs of the whole student. 

The Programme for International Student Assessment (PISA) argues for a broadening of what is taught to create a ‘new mathematical literacy’. This new definition focuses on using mathematics to solve real-world problems and identifies mathematical reasoning as a central aspect of math literacy.

The challenge for educators and edtech is not solely to introduce students to new concepts but to create opportunities for reflection and conversation about how they approach these new concepts. Share on X

The resulting challenge for educators and edtech is not solely to introduce students to new concepts but to create opportunities for reflection and conversation about how they approach these new concepts. 

Metacognition techniques

However, bringing these new competencies to life raises questions about how we currently teach.

Providing all students with an opportunity to communicate their knowledge has its challenges. For one, mathematical language is technical and precise, and so many students have a difficult time expressing in words what they have written on paper. In addition, students with different personality types or learning styles may excel in different types of activities or environments. 

The goal should therefore be to foster greater opportunities for metacognition – supporting students’ thinking about their options, their choices, and their results. Edtech needs to be part of the answer if we are to personalize the teaching experience at scale. 

When using metacognition students may think about:

• Options: What strategies they could use
• Choices: What strategies they will use
• Outcomes: How effective their choices were
• Planning: Whether to continue with or change their chosen strategies 

By capturing these reflections,  both students and teachers can increase their awareness of the learning process. Variety in assessment question types is important to enabling that shift. 

Assessment for learning

Well-designed online formative assignments create opportunities for every student to succeed. In addition to consolidating learning, they can give the student a chance to reflect on their own understanding – thereby changing mindsets and learning outcomes. 

For low-stakes assessments, students can receive immediate feedback as they practice their skills with autoscoreable math question types. Teachers can also set open-ended questions and test students’ conceptual knowledge with math essay question types.

By utilizing audio and video question types, every student has a voice and the opportunity to communicate their knowledge and explain their reasoning. Visual learners will benefit from assignments that include drawing and graphing question types. Including assignments after examinations that ask students to reflect on how they prepared and performed on the exam can offer further assistance in students’ future success.

Well-designed online formative assignments create opportunities for every student to succeed. They can give the student a chance to reflect on their own understanding – thereby changing mindsets and learning outcomes. Share on X

These assessments, when administered during the learning process, can benefit both students and teachers. Students can identify their strengths and weaknesses and see that their understanding is not fixed and will improve over time. With the appropriate analytics, teachers can discover gaps in students’ understanding early and adjust accordingly. 

Math and edtech 

More effective math education, driven by fresh perspectives (such as those outlined by PISA and individual researchers) and facilitated by a wave of fresh investment in technology, is gradually leading to the transformation of the math learning experience. 

Having the capacity to support metacognitive activities in learning products gives students greater agency over their development and performance. 

While these open-ended assignments don’t teach students mathematical content per se, they bolster students’ confidence in their own potential to deepen their math intelligence.

References:

NAEP Mathematics Report Card

PISA 2021 Mathematics: A Broadened Perspective